Robust satisficing model with Sinkhorn distance

We study the robust satisficing model with Sinkhorn distance. The modeling paradigm based on Sinkhorn distance leads to a continuous worst-case distribution which is consistent with practical problems. Under some mild assumptions, the robust satisficing model with Sinkhorn distance can be reformulated as a convex program. Furthermore, we give a conic optimization reformulation when the sample space is finite. We apply the augmented Lagrangian method to solve the reformulation of the robust satisficing model with Sinkhorn distance. Finally, we report some preliminary numerical test results about the out-of-sample performance in the setting of the data-driven newsvendor problem. The robust satisficing model with Sinkhorn distance outperforms the distributionally robust optimization model, the distributionally robust optimization model with Sinkhorn distance and the robust satisficing model with Wasserstein distance.